The Fibonacci sequence of numbers was described in a mathematics book by Leonardo da Pisa (Fibonacci) called Liber Abaci. The n-th element of the sequence represents the number of pairs of rabbits at the start of the n-th month, beginning with a single pair, given that in every month each pair bears a new pair which becomes productive from the second month on. It is a common example used in Education to teach recursion.

Here are the first 14 Fibonacci numbers, starting with F(0):
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...
and various Common Lisp implementations for the computation of the nth element of the sequence, structured similarly to the Factorial page:

Q: In the Winston & Horn book, n for the two above functions is n+1. Is there some reason for NOT having e.g.(expt (/ (- 1 (sqrt 5)) 2) (+ n 1))) ?
A: Some authors still use a deprecated definition of the Fibonacci sequence, the one that begins with 1, 1 instead of 0, 1. Please see the definition and especially the
closed form.
Also, most books that touch on this topic (Donald Knuth's TAOCP for instance).

Q: Do we have any reason to keep the first implementation instead of the second one based on the Binet formula? --Cornel

Caution: Due to limitations in floating-point representation precision, this last version works - (truncate (fib n)) is correct - only for n < 32. From that point on, the error rises exponentially approximately like this: new_error = old_error * (5 / 3)
So, if for n = 32 the error is 1.25, for n = 99 the error is 4.2221247E14. I determined this using CLISP 2.33.2 under GNU Linux on IA32.
This can be improved by using 5.0d0 instead of 5, which ensures the use of
double-float. CLISP 2.33.2 computes correct values (using (round (fib n)) for
n ≤ 75.